In a bowl combine the deboned and shredded chicken, cheese(s), red onion, green onion, tomatoes, cilantro, jalapeno peppers and fresh lime. Season to taste with salt and pepper. To assemble and cook a quesadilla, spread or brush the softened butter on one side of two tortillas. Place one tortilla butter-side down in a medium-heated 10-inch or larger skillet. Spread 1/4 of the chicken mixture on top of the tortilla and top with the remaining tortilla, butter-side up. Cook until the bottom tortilla is nice and golden brown, using a pancake turner, carefully turn the quesadilla over and cook until nicely golden brown. Repeat process 3 more times with remaining tortillas and chicken mixture. To serve, cut each quesadilla into 8 wedges and serve with a dollop of sour cream and salsa on the side.